Problem: Multiply the following complex numbers: $({-1+i}) \cdot ({5})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1+i}) \cdot ({5}) = $ $ ({-1} \cdot {5}) + ({-1} \cdot {0}i) + ({1}i \cdot {5}) + ({1}i \cdot {0}i) $ Then simplify the terms: $ (-5) + (0i) + (5i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -5 + (0 + 5)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -5 + (0 + 5)i - 0 $ The result is simplified: $ (-5 - 0) + (5i) = -5+5i $